Details

sample27.0ms

Algorithm

intervals

Results

8.0ms	250×	body	80	valid
2.0ms	19×	body	640	valid
1.0ms	12×	body	320	valid
1.0ms	7×	body	1280	valid
0.0ms	7×	body	160	valid

simplify89.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (8.0ms)

Iter	Nodes	Cost
0	20	6
1	45	6
2	116	5
3	324	5
4	861	5
5	1907	5
6	4560	5
7	5001	5

prune9.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 10.5b

Counts

2 → 2

localize14.0ms

Local error

Found 2 expressions with local error:

0.0b	(/ (- y x) (- a t))
12.6b	(fma (/ (- y x) (- a t)) (- z t) x)

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt` `*-un-lft-identity`
25×	`times-frac`
14×	`add-cube-cbrt`
12×	`distribute-lft-out--` `difference-of-squares`
5×	`associate-/r` `associate-/l`
4×	`add-exp-log` `add-cbrt-cube`
2×	`pow1` `expm1-log1p-u` `flip3--` `associate-/r/` `flip--` `log1p-expm1-u` `associate-/l/` `add-log-exp`
1×	`cbrt-undiv` `frac-2neg` `div-sub` `div-exp` `clear-num` `fma-udef` `div-inv`

Counts

2 → 64

Calls

2 calls:

10.0ms	(/ (- y x) (- a t))
1.0ms	(fma (/ (- y x) (- a t)) (- z t) x)

series152.0ms

Counts

2 → 6

Calls

2 calls:

54.0ms	(/ (- y x) (- a t))
98.0ms	(fma (/ (- y x) (- a t)) (- z t) x)

simplify69.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (23.0ms)

Iter	Nodes	Cost
0	269	450
1	734	425
2	2488	423
3	5002	423

prune240.0ms

Filtered

70 candidates to 51 candidates (72.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	58	12	70
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	59	13	72

Merged error: 5.8b

Counts

72 → 13

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- a t))
0.3b	(* (- y x) (/ 1 (- a t)))
12.6b	(fma (* (- y x) (/ 1 (- a t))) (- z t) x)

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
32×	`times-frac`
23×	`add-cube-cbrt`
21×	`associate-r`
16×	`add-exp-log`
10×	`add-cbrt-cube`
8×	`distribute-lft-out--` `difference-of-squares`
6×	`pow1`
5×	`associate-l` `associate-/r*`
4×	`flip3--` `div-exp` `prod-exp` `associate-/r/` `flip--`
3×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l*` `add-log-exp` `unswap-sqr`
2×	`cbrt-undiv` `frac-times` `rec-exp` `1-exp` `associate-*l/` `cbrt-unprod` `div-inv`
1×	`pow-flip` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `un-div-inv` `-commutative` `fma-udef` `inv-pow`

Counts

3 → 105

Calls

3 calls:

6.0ms	(/ 1 (- a t))
15.0ms	(* (- y x) (/ 1 (- a t)))
1.0ms	(fma (* (- y x) (/ 1 (- a t))) (- z t) x)

series194.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(/ 1 (- a t))
60.0ms	(* (- y x) (/ 1 (- a t)))
96.0ms	(fma (* (- y x) (/ 1 (- a t))) (- z t) x)

simplify51.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	351	602
1	1495	525
2	5001	481

prune314.0ms

Filtered

114 candidates to 68 candidates (59.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	110	4	114
Fresh	3	9	12
Picked	1	0	1
Done	0	0	0
Total	114	13	127

Merged error: 5.8b

Counts

127 → 13

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- y x) (- a t))
2.2b	(+ (* (/ (- y x) (- a t)) (- z t)) x)
4.3b	(* (/ (- y x) (- a t)) (- z t))

rewrite297.0ms

Algorithm

rewrite-expression-head

Rules

102×	`add-sqr-sqrt`
97×	`*-un-lft-identity`
51×	`add-cube-cbrt` `times-frac`
36×	`prod-diff`
31×	`associate-l`
23×	`distribute-lft-out--` `difference-of-squares`
22×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-r` `associate-/r` `flip--` `associate-/l` `add-log-exp`
4×	`sub-neg` `associate-/r/`
3×	`expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-times` `associate-*r/` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `fma-def` `frac-2neg` `flip3-+` `div-sub` `pow-prod-down` `associate-l/` `clear-num` `sum-log` `-commutative` `flip-+`

Counts

3 → 170

Calls

3 calls:

9.0ms	(/ (- y x) (- a t))
17.0ms	(+ (* (/ (- y x) (- a t)) (- z t)) x)
263.0ms	(* (/ (- y x) (- a t)) (- z t))

series438.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(/ (- y x) (- a t))
157.0ms	(+ (* (/ (- y x) (- a t)) (- z t)) x)
226.0ms	(* (/ (- y x) (- a t)) (- z t))

simplify93.0ms

Algorithm

egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	684	1508
1	2581	1283
2	5003	1263

prune518.0ms

Filtered

179 candidates to 118 candidates (65.9%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	171	8	179
Fresh	4	8	12
Picked	1	0	1
Done	0	0	0
Total	176	16	192

Merged error: 5.7b

Counts

192 → 16

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- z t) (- a t))
2.0b	(+ (* (- y x) (/ (- z t) (- a t))) x)
2.6b	(* (- y x) (/ (- z t) (- a t)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-sqr-sqrt`
73×	`*-un-lft-identity`
51×	`times-frac`
31×	`associate-r`
27×	`add-cube-cbrt`
23×	`distribute-lft-out--` `difference-of-squares`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `flip3--` `associate-l` `associate-/r` `flip--` `associate-/l` `add-log-exp`
4×	`associate-/r/`
3×	`expm1-log1p-u` `log1p-expm1-u`
2×	`cbrt-undiv` `frac-times` `div-exp` `associate-*l/` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `fma-def` `frac-2neg` `flip3-+` `div-sub` `associate-r/` `pow-prod-down` `clear-num` `sum-log` `-commutative` `flip-+`

Counts

3 → 126

Calls

3 calls:

9.0ms	(/ (- z t) (- a t))
14.0ms	(+ (* (- y x) (/ (- z t) (- a t))) x)
19.0ms	(* (- y x) (/ (- z t) (- a t)))

series348.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(/ (- z t) (- a t))
164.0ms	(+ (* (- y x) (/ (- z t) (- a t))) x)
128.0ms	(* (- y x) (/ (- z t) (- a t)))

simplify74.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 2 (61.0ms)

Iter	Nodes	Cost
0	491	904
1	2052	854
2	5003	852

prune368.0ms

Filtered

135 candidates to 94 candidates (69.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	130	5	135
Fresh	7	8	15
Picked	1	0	1
Done	0	0	0
Total	138	13	151

Merged error: 3.8b

Counts

151 → 13

regimes318.0ms

Accuracy

17.6% (6.3b remaining)

Error of 10.2b against oracle of 3.9b and baseline of 11.6b

bsearch119.0ms

Steps

Iters	Range		Point
8	7.40395357533121e-198	7.391279573739562e-194	6.966124702757521e-194
9	-3.987266020246131e-224	-3.7164576505082027e-233	-2.9108958045626465e-224

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	30
1	34	30

end0.0ms

sample728.0ms

Algorithm

intervals

Results

264.0ms	7757×	body	80	valid
68.0ms	501×	body	640	valid
53.0ms	291×	body	1280	valid
36.0ms	391×	body	320	valid
15.0ms	246×	body	160	valid
3.0ms	16×	body	2560	valid